Problem: Simplify the following expression: $r = \dfrac{p}{8} + \dfrac{4p}{9}$
Solution: In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $8$ and $9$ $\lcm(8, 9) = 72$ $ r = \dfrac{9}{9} \cdot \dfrac{p}{8} + \dfrac{8}{8} \cdot \dfrac{4p}{9} $ $r = \dfrac{9p}{72} + \dfrac{32p}{72}$ $r = \dfrac{9p +32p}{72}$ $r = \dfrac{41p}{72}$